Too Simple

OVERSIMPLIFICATION
Some very common, often unrecognized, problems

OFOT: When two factors are essential (like the length and width of a corn field for calculating its area) it's oversimplification to declare one false statement and one true statement (OFOT) like this: "It not the width that determines the area; it's the length!" "Guns don't kill people; people kill people." Sure, OFOT is absurd; but it's heard over and over again in daily discussions. Furthermore, it's about the simplest case of a much larger family of errors of omission in situations of multiple influences—which is just about every situation.

Necessity vs. Sufficiency: Rejecting a necessity on the grounds that it isn't sufficient is oversimplification. ("That no panacea; ignore it!" "Science cannot answer questions about human values, so science is just an alternative reality which I don't choose to accept." ) Claiming sufficiency on the basis of necessity is oversimplification. ("We are seeking the simple differential equations that describe, predict, and explain everything.") These are two kinds of improperly inverted implications.

Implication, the logical relationship: (Necessity vs sufficiency is a special case.) If A implies B, A is sufficient for B; but the inverse relationship, B implies A, means that A is necessary for B. Notice that when expressed in this abstract way, the relationships are at least a little confusing to a large fraction of people—but are "perfectly obvious" to a small fraction of people. On the other hand, specific, familiar examples are quite "obvious" to a majority. For example, "If there is a potato in the box, then there is a vegetable in the box" (potato is sufficient for being a vegetable) is pretty obvious to most. Furthermore, "If there is a vegetable in the box, there may or may not be a potato in the box" (a vegetable is not necessarily a potato) is equally obvious. For those relatively few who "see" the abstract expression, a specific kind of "perception of abstraction" exists. Those individuals have developed a sense for implication which turns out to be a powerful tool for "seeing" certain science concepts and even for extending them. Without that "sixth sense," a person may see implication, and perhaps even science itself, as "merely a social construct with no universal principles..." [SEE]

Familiar statements that indicate misunderstanding. "The Singles" is a persistent, pervasive, and pernicious infection of human use of knowledge. "Perceptions of abstractions" that organize our thoughts about multi-element relationships can help vaccinate us against "The Singles." This kind of "perception" is remarkably resistant to teaching and learning, and that fact contributes strongly to the perceived difficulty of science and mathematics. On our Web site we refer to this problem as "exploring the edges of human comprehension." Our raw material for examining this problem and for constructing a useful theory of the edges of human comprehension is a collection of "Statements that give little clues that something wasn't really quite understood." This collection is at our Misunderstandings Workshop. We invite everyone to contribute to this collection and to the interpretations suggested. If you have a Web site that discusses such matters we would like to incorporate links to your site.

Rank-orderable measure. Comparatives and superlatives require scalar (single-component) measure. Most measures have multiple components. Comparatives and superlatives rarely have the meaning intended. More often they express personal biases. Overcoming scalar-limited perception of measurement is a challenge at the edge of human comprehension

"For every complex question, there's an answer
that's simple, neat, and wrong."
...H. L. Mencken

PERSISTENT

PERVASIVE

PERNICIOUS

PRE-SCIENTIFIC

PREDICTABLE

PREPOSTEROUS

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